Self-Localized Liquid Crystal Micro-Droplet Arrays on Chemically Patterned Surfaces

: Liquid crystal (LC) micro-droplet arrays are elegant systems that have a range of applications, such as chemical and biological sensing, due to a sensitivity to changes in surface properties and strong optical activity. In this work, we utilize self-assembled monolayers (SAMs) to chemically micro-pattern surfaces with preferred regions for LC occupation. Exploiting discontinuous dewetting, dragging a drop of ﬂuid over the patterned surfaces demonstrates a novel, high-yield method of conﬁning LC in chemically deﬁned regions. The broad applicability of this method is demonstrated by varying the size and LC phase of the droplets. Although the optical textures of the droplets are dictated by topological constraints, the additional SAM interface is shown to lock in inhomogeneous alignment. The surface effects are highly dependent on size, where larger droplets exhibit asymmetric director conﬁgurations in nematic droplets and highly knotted structures in cholesteric droplets.


Introduction
Due to their optical activity, LCs in confined geometries are important to a variety of current technologies. In polymer-dispersed LCs, micron-sized LC droplets are directed to either scatter or transmit light by altering the molecular orientation using an external electric field [1], a switching mechanism which has been utilized in smart windows [2]. Microencapsulated cholesteric LCs have a long history as thermochromic paint used for surface thermography in structural materials, microelectronics, fluid mechanics, and medicine [3]. More recently, cholesteric droplets have been exploited to create photonic arrays [4].
LCs also provide a platform for chemical and biological sensing [5,6]. Due to longrange orientational order, the absorption of a small quantity of molecules on LC interfaces can change the surface-anchoring conditions of the LC molecules and lead to changes in the optical properties at the macro-scale. Microfluidic devices that utilize LCs [7,8] are becoming popular because they can be easily incorporated into sensor networks or lab-on-a-chip systems, which are highly desirable for environmental science, forensics, biological warfare, and point-of-care diagnostics. Such devices need high sensitivity to target molecules, fast response to change, portable size, and must be economically and environmentally friendly.
The sensitivity of LCs to surface properties is dependent on LC material properties, surface anchoring, and geometric confinement [9]. The latter is a continuously-tunable variable that changes the LC sensitivity by controlling the ratio of exposed surface area to volume effects of the LC. In free-floating spherical droplets, the ratio is 1/(3r), where r is the radius of the droplet. When immobilized as a spherical cap on a surface, the ratio is a more complex function that depends on the contact angle of the droplet. Furthermore, the asymmetry of surfaces, i.e., substrate-liquid vs. liquid-vapor, provides another layer of complexity. The interplay between long-range interaction length of the LCs and the confinement surface effects creates a rich tapestry of defect structures and transitions.
There are several methods for generating fluid arrays; the most common for LC microarrays use inkjet printing [4,8]. Another attractive option is to use chemically patterned surfaces to exploit chemical pinning [10,11] of a fluid sliding on a surface that results in discontinuous dewetting [12] of a fluid moving over the surface, leaving self-localized microdroplets on the surface [13][14][15]. In monophilic systems, hydrophilic regions are patterned on hydrophobic or syperhydrophobic surfaces, and the fluid can either be applied by rolling drops across the surface or via dipcoating [16]. This method has been used with aqueous fluids for a wide variety of biological applications [17], with polymers to generate channel waveguides [18] and multiphasic particles [19] and, drawing inspiration from fog-basking Namib desert beetles such as Stenocara gracilipes, Onymacris unguicularis and Physosterna cribripes [20,21], for water harvesting [22], fog-free mirrors, and cancer research [23]. However, chemical patterning to localize LC has only recently been shown in literature [24]. Thermotropic LCs tend to be amphiphilic, making it difficult to find surfaces that are chemically LC-phobic (a contact angle θ c > 90 • ).
In this work, we explored the ability of LC to self-localize via chemical pinning [10] on µ-contact printed surfaces [25] using two LC-philic (θ c < 90 • ) inks by maximizing the disparity between static contact angles. We note that the wettability of the surface is tied to the molecular orientation on the surface, with planar alignment generally being more favorable than homeotropic alignment. In nematic LCs, we observe optical structures that reflect formation dynamics, surface inhomogeneities, and inherent topological constraints. Cholesteric systems exhibit unique knotting properties that are tied to the size of the chiral pitch inside the drops, able to transform from an ordered spiral to a highly knotted optical texture.

Materials and Methods
For contact angle measurement, Au-coated glass was immersed in 1 mM ethanolic solutions of thiol-terminated molecules for one hour for self-assembly, and then a drop of the LC 5CB was placed on the surface using a syringe and imaged using a custom setup.
Chemically patterned surface were fabricated using µ-contact printing (µCP) [25]. To make master molds, negative resist SU8 was spin-coated onto a Si wafer and patterned using contact lithography with a custom photomask from Photo Sciences, Inc. (Torrance, CA, USA), whose design is shown in Figure S1. The molds were coated with 10:1 volume mixture of precursor:crosslinker of polydimethylsiloxane (PDMS, Slygard 184, Midland, DX, USA), which was de-gassed and cured at 65 • C for 12 h. The PDMS was then carefully pealed from the SU8 mold, resulting in an elastomeric stamp. The stamp was coated with 20 µL of 1 mM ethanolic solution of the thiol-terminated molecular ink mercaptododecanoic acid (MDA, Sigma-Aldrich, St. Louis, MO, USA). After 30 s, the bulk solution was blown off with a stream of air. The stamp was then brought into contact with an Au-coated glass slide for 30 s. The ink molecules absorbed onto the Au surface via thiol-metal bonds, forming a monolayer. The glass slide was rinsed thoroughly with ethanol and then submerged in a 1 mM ethanol solution of thiol-terminated octodecanethiol (ODT, Sigma-Aldrich) background molecules for one hour.
Because self-assembled monolayer (SAM) formation is strongly influenced by diffusion properties of constituent molecules [26], the stamping time is an important parameter. We empirically determined that the optimal stamping time is around 30 s in our system. At higher stamping times, the resulting droplets are larger than the stamp features, which is a result of diffusion along the surface. At shorter times, the LC droplet shapes becomes irregular and non-uniform.
Polarized optical micrographs (POMs) were taken using a custom inverted microscope setup built using optomechanics components with Mitutoyo Plan Apochromat long working distance objectives and a DCC1645C-HQ camera (Thorlabs, Inc., Newton, NJ, USA). A syringe is suspended horizontally next to the stage, with a 90-degree bent needle so that Polarized optical micrographs (POMs) were taken using a custom inverted microscope setup built using optomechanics components with Mitutoyo Plan Apochromat long working distance objectives and a DCC1645C-HQ camera (Thorlabs, Inc., Newton, NJ, USA). A syringe is suspended horizontally next to the stage, with a 90-degree bent needle so that the tip is normal to the sample surface. The light source above the sample is polarized and an analyzer in front of the camera allows for polarized microscopy. The stage is controlled manually using a micrometer screw while the syringe and microscope components remain stationary.

5CB-SAM Interaction
The static contact angle of the droplets, θc, on binary chemically patterned surfaces, can be broken down into three distinct conditions [27]. As is shown in Figure 1, the liquid is designated as α, the gaseous environment is β, the high-wettability domain is γ, and the low-wettability domain is δ. If the droplet is fully contained within the γ-domain ( Figure  1a), θc = θc,γ. In the case where the droplet is larger than the γ-domain and its edges are located on the δ-domain (Figure 1b), the contact angle θc = θc,δ. Finally, if the droplet is pinned at the interface between the γ-and δ-domains (Figure 1c), the contact angle takes on an intermediate value θc,γ < θc < θc,δ and is dependent on the volume of the droplet. Chemical structures of 5CB, MDA, and ODT are shown in Figure 1d. First, we observed the behavior of 5CB on the hydrophilic MDA. The unconjugated and non-polar dodecyl moiety was used to isolate 5CB from the metallic gold surface. The carboxylic acid terminal group creates an even, polar surface for the 5CB molecules. A schematic of the system is shown in Figure 1e. The 5CB-MDA interaction in air shows high wettability with a contact angle <7°, which is consistent with previous reports of 5CB on carboxylic acid-terminated surfaces in the literature [28]. Between crossed polarizers we observe that the 5CB takes on a planar orientation on the surface. The high wettability suggests that the planar 5CB-MDA interaction is stronger than the homeotropic 5CB-air interaction. Distilled H2O on MDA exhibited a contact angle of 35°.
We also examined the behavior of 5CB on SAMs of ODT. The purpose of ODT SAMs is to insulate the 5CB from the metallic surface with a non-polar interface. 5CB shows a Chemical structures of 5CB, MDA, and ODT are shown in Figure 1d. First, we observed the behavior of 5CB on the hydrophilic MDA. The unconjugated and non-polar dodecyl moiety was used to isolate 5CB from the metallic gold surface. The carboxylic acid terminal group creates an even, polar surface for the 5CB molecules. A schematic of the system is shown in Figure 1e. The 5CB-MDA interaction in air shows high wettability with a contact angle <7 • , which is consistent with previous reports of 5CB on carboxylic acid-terminated surfaces in the literature [28]. Between crossed polarizers we observe that the 5CB takes on a planar orientation on the surface. The high wettability suggests that the planar 5CB-MDA interaction is stronger than the homeotropic 5CB-air interaction. Distilled H 2 O on MDA exhibited a contact angle of 35 • .
We also examined the behavior of 5CB on SAMs of ODT. The purpose of ODT SAMs is to insulate the 5CB from the metallic surface with a non-polar interface. 5CB shows a lower wettability on the ODT surface with a contact angle~60 • . Using polarized optical microscopy, we observe that the orientation is homeotropic. This is likely due to the alkyl chain of the 5CB inserting into the ODT layer [29], as is shown in Figure 1e. Distilled H 2 O has low wettability on ODT with a contact angle larger than 100 • , verifying that there is a poor interaction of the SAM with polar groups.

Self-Localization of LC
Droplet arrays were formed on the patterned SAM by taking advantage of the chemical pinning effect [10,11]. The process occurs in four stages (Figure 2a). First, a large (several mm diameter) drop is placed on the patterned surface using a syringe and takes on the static contact angle of the ODT ink, θ c,δ . When the substrate beings to move, the drop is anchored by the syringe and gets stretched until the back of the drop take on its receding contact angle for the δ-surface θ rδ . At this point, the back edges of the drop begin to slide across the surface with a constant contact angle θ rδ until it reaches a γ-domain. Because θ rδ > θ rγ , the drop becomes pinned at the back of the domain as it gets further stretched while the rest of the drop continues to slide along the sides of the domain. Near the end of the process, only a narrow fluid bridge remains between the pinned fluid and the moving drop, highlighted in Figure 2b (see Supplementary Materials Video S1). When this breaks, a droplet is left in the wake of the large drop with a static contact angle θ c,γ < θ c < θ c,δ . Droplets that have a contact angle smaller than θ c,γ at the time of formation will contract on the γ-domain, as is shown in the center of the ESEM image in Figure 2c, where the droplets in black are shown sitting on larger dark-grey regions of the MDA ink. lower wettability on the ODT surface with a contact angle ~60°. Using polarized optical microscopy, we observe that the orientation is homeotropic. This is likely due to the alkyl chain of the 5CB inserting into the ODT layer [29], as is shown in Figure 1e. Distilled H2O has low wettability on ODT with a contact angle larger than 100°, verifying that there is a poor interaction of the SAM with polar groups.

Self-Localization of LC
Droplet arrays were formed on the patterned SAM by taking advantage of the chemical pinning effect [10,11]. The process occurs in four stages (Figure 2a). First, a large (several mm diameter) drop is placed on the patterned surface using a syringe and takes on the static contact angle of the ODT ink, θc,δ. When the substrate beings to move, the drop is anchored by the syringe and gets stretched until the back of the drop take on its receding contact angle for the δ-surface θrδ. At this point, the back edges of the drop begin to slide across the surface with a constant contact angle θrδ until it reaches a γ-domain. Because θrδ > θrγ, the drop becomes pinned at the back of the domain as it gets further stretched while the rest of the drop continues to slide along the sides of the domain. Near the end of the process, only a narrow fluid bridge remains between the pinned fluid and the moving drop, highlighted in Figure 2b (see Supplementary Materials Video S1). When this breaks, a droplet is left in the wake of the large drop with a static contact angle θc,γ < θc < θc,δ. Droplets that have a contact angle smaller than θc,γ at the time of formation will contract on the γ-domain, as is shown in the center of the ESEM image in Figure 2c, where the droplets in black are shown sitting on larger dark-grey regions of the MDA ink.  the droplet. This can be controlled chemically by the inks used or by the speed of the drop, because receding contact angles have varying velocity dependence. In this work, we used a velocity of~1 µm/s, which was roughly controlled by manually turning a micrometer screw on a translation stage. We noticed that the droplets that formed at the periphery of the drop tended to be thinner than those formed near the center, which is shown in Figure 2d. We theorize that this is due to the curvature of the drop at the periphery, which results in a receding edge that is not perpendicular to the motion. As a result, the fluid bridge is larger and fluid on the γ-domain deforms further before breaking off from the main drop.
The influence of fluid anisotropy on this process is beyond the scope of this work. Although we would expect that the difference in alignment on ODT and MDA, in addition to the LC's elastic response to deformation, could play a role in either suppressing or enhancing droplet self-localization, our understanding of the process does not differentiate between isotropic and anisotropic fluids.

Droplets of Nematic LC
The topological confinement of LC droplets on surfaces is sensitive to the anchoring of the constituent molecules at the surface. As a result, observing drop topology using POM is commonly used to determine local surface anchoring conditions [30][31][32][33][34]. Topological constraints of a homeotropically aligned curved air-5CB surface and planar degenerate anchoring at the MDA-5CB surface results in a single +1 boojum defect embedded at the center of the SAM. This leads to a continuous four-brush pattern, shown in Figure 3a-c. In larger droplets with diameters~30 µm, the location of the defect can be significantly off-center, as is shown in Figure 3a. This is due to surface inhomogeneities at the surface that pin the defect.  As the diameter decreases (Figure 3b,c), the homeotropically aligned curved surface generates more internal strain on the LC orientational elasticity and pushes the defects more reliably into the center. As the size decreases further, the mismatch of the surface anchoring conditions breaks the order of the LC, leading to a complete loss of anisotropy, which can be seen in Figure 3d. We expect that the diameter required to achieve homogeneous droplet structures (~15 μm) is strongly dependent on the contact angle, but our results are consistent with those demonstrated in micro-wells of ~10 μm [35].

Droplets of Cholesteric LC
In the bulk, cholesteric LC takes on a chiral order to minimize its free energy. By confining this LC into μm-sized droplet arrays, we observed the effect this has on the As the diameter decreases (Figure 3b,c), the homeotropically aligned curved surface generates more internal strain on the LC orientational elasticity and pushes the defects more reliably into the center. As the size decreases further, the mismatch of the surface anchoring conditions breaks the order of the LC, leading to a complete loss of anisotropy, which can be seen in Figure 3d. We expect that the diameter required to achieve homogeneous droplet structures (~15 µm) is strongly dependent on the contact angle, but our results are consistent with those demonstrated in micro-wells of~10 µm [35].

Droplets of Cholesteric LC
In the bulk, cholesteric LC takes on a chiral order to minimize its free energy. By confining this LC into µm-sized droplet arrays, we observed the effect this has on the POM texture. The natural pitch of the LC is 1 µm at room temperature. In small droplets of around 10 µm (Figure 4a), the four-brush pattern can be easily seen as the surface alignment dominates the internal elastic energy of the droplet. As the droplets become larger (Figure 4b), the brush pattern becomes distorted as the chiral contribution becomes more pronounced. Finally, in droplets around 30 µm in diameter, the POM shows a highly knotted complex metastable state [36,37] with defect lines pinned at the SAM interface and twisting through one another.  Using temperature to vary the pitch of the LC, we further explored the effect of confinement. With a custom mixture, the pitch increases with temperature. As the 30 μm droplets are heated, the knotted structure generally remains due to strongly pinned defect lines at the SAM surface until the fluid transitions to the isotropic phase (see Supplementary Materials Video S2). However, as the droplet is cooled from the isotropic, the large pitch cholesteric phase appears as a spiral in the center of the droplet (Figure 4f, Supplemental Materials Video S3), with a region of isotropic LC in the regions of smaller thickness. The spiral texture is similar to that of the Frank-Pryce structure observed in spherulites [38] and spherical droplets [9]. However, in the case of spherical caps, the characteristic defect line from the Frank-Pryce structure is removed by the surface and a simple spiral remains. This is likely due to surface-induced disorder at the SAM interface, which keeps the LC in the isotropic phase, reducing the surface anchoring energy and allowing Using temperature to vary the pitch of the LC, we further explored the effect of confinement. With a custom mixture, the pitch increases with temperature. As the 30 µm droplets are heated, the knotted structure generally remains due to strongly pinned defect lines at the SAM surface until the fluid transitions to the isotropic phase (see Supplementary Materials Video S2). However, as the droplet is cooled from the isotropic, the large pitch cholesteric phase appears as a spiral in the center of the droplet (Figure 4f, Supplemental Materials Video S3), with a region of isotropic LC in the regions of smaller thickness. The spiral texture is similar to that of the Frank-Pryce structure observed in spherulites [38] and Crystals 2022, 12, 13 7 of 9 spherical droplets [9]. However, in the case of spherical caps, the characteristic defect line from the Frank-Pryce structure is removed by the surface and a simple spiral remains. This is likely due to surface-induced disorder at the SAM interface, which keeps the LC in the isotropic phase, reducing the surface anchoring energy and allowing the chiral structure to resolve without forming additional defects. As the droplet cools further, the spiral grows (Figure 4g,h) until it reaches an abrupt transition where the highly knotted structure again appears (Figure 4i). This final step corresponds to the transition of the LC to the nematic phase at the surface.

Conclusions
In this work, we exploited the properties of strong planar and weak homeotropic inks to chemically pattern surfaces to induce self-localization of discrete LC droplets. We presented a phenomenological understanding of this process based on pinning of receding contact angles by two inks that would traditionally be considered LC-philic. The method allowed us to generate a range of LC droplet arrays with great fidelity while varying droplet diameters to explore the effect of geometric confinement on LC topology. Using POM, we observed both the effect of droplet size on liquid crystals and the effect of varying the pitch of a cholesteric LC.
This method can easily be adapted to self-localize LCs with varying properties simultaneously on the surface using multiple syringes. It can enable the roll-to-roll processing of bio/chemo-responsive LC arrays and optical devices.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/cryst12010013/s1, Video S1: Dragged Drop.mp4; Video S2: Droplet Heating.mp4; Video S3: Droplet Cooling.mp4; Figure S1: Photomask layout for µ-contact printing (µcp) with circle diameters and periods in the table on the left. The distance between adjacent circles is 30 µm; Figure S2: Microscope images of the elastomeric stamp used for µcp (top) compared to the self-localized LC droplet images (bottom 2 rows). Measured sizes are shown at the bottom of the images. Colored circles are drawn as guides from the elastomeric stamps; Figure